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We re-derive the expression for the heat current for a classical systemsubject to periodic boundary conditions and show that it can be written as asum of two terms. The first term is a time derivative of the first moment ofthe system energy density while the second term is expressed through the energytransfer rate through the periodic boundary. We show that in solids the secondterm alone leads to the same thermal conductivity as the full expression forthe heat current when used in the Green-Kubo approach. More generally, energypassing though any surface formed by translation of the original periodicboundary can be used to calculate thermal conductivity. These statements areverified for two systems: crystalline argon and crystals of argon and kryptonforming an interface.

On the definition of heat current for periodic systems and its implications for simulations of thermal conductivity in solids